Question

cos(sin-1 x + cos
-1​

Answer 1

Answer: 1

To find:

$\sf cos(sin^{-1}x+cos^{-1}x)$

Identity used:

$\sf sin^{-1}x+cos^{-1}x=\dfrac{\pi}{2}$

Explanation:

$\textsf{According to the question,}$

$\Rightarrow \sf cos(sin^{-1}x+cos^{-1}x)$

$\textsf{Using the identity,we get:}$

$\Rightarrow \sf cos\dfrac{\pi}{2}$

$\Rightarrow \sf cos\:90^{\circ}$

$\Rightarrow\boxed{ \sf 1}$

Hence, the value of cos(sin⁻¹+cos⁻¹) is 1.